May 16, 2013

Researchers have for the first time directly observed a rare quantum effect that produces a repeating butterfly-shaped energy spectrum, confirming the longstanding prediction of the quantum fractal energy structure known as Hofstadter's butterfly.

First predicted by American physicist Douglas Hofstadter in 1976, the Hofstadter butterfly emerges when electrons are confined to a two-dimensional sheet, and subjected to both a periodic potential energy and a strong magnetic field.

The Hofstadter butterfly is a fractal pattern, meaning it contains shapes that repeat on smaller and smaller size scales. Fractals are common in classical systems such as fluid mechanics, but are rare in the quantum mechanical world.

In fact, the Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics, although until now there has been no direct experimental proof of this spectrum.

Previous efforts to study the Hofstadter butterfly attempted to use artificially created structures to achieve the required periodic potential energy. These studies produced strong evidence for the Hofstadter spectrum, but were dramatically hindered by the difficulty in creating structures that were both small and perfect enough to allow detailed study.

To map the graphene energy spectrum, the researchers then measured the electronic conductivity of the samples at very low temperatures in extremely strong magnetic fields up to 35 Tesla (consuming 35 megawatts of power) at the National High Magnetic Field Laboratory.

The measurements show the predicted self-similar patterns, providing the best evidence to date for the Hofstadter butterfly, and providing the first direct evidence for its fractal nature.

"This is a huge leap forward–our observation that interplays between competing length scales result in emergent complexity provides the framework for a new direction in materials design. And such understanding will help us develop novel electronic devices employing quantum engineered nanostructures."

"The opportunity to confirm a 40-year-old prediction in physics that lies at the core of most of our understanding of low-dimensional material systems is rare, and tremendously exciting," said Dean.

"Our confirmation of this fractal structure opens the door for new studies of the interplay between complexity at the atomic level in physical systems and the emergence of new phenomenon arising from complexity."